Examples: Solve the following LPPs by simplex method
1) \( \operatorname{Max} Z=2 x_{1}+4 x_{2} \); s.t. \( 2 x_{1}+3 x_{2} \leq 48 ; x_{1}+3 x_{2} \leq 42 ; x_{1}+x_{2} \leq 21 ; x_{1}, x_{2} \geq 0 \)
2) \( \operatorname{Max} Z=4 x_{1}+10 x_{2} \); s.t. \( 2 x_{1}+x_{2} \leq 50 ; 2 x_{1}+5 x_{2} \leq 100 ; 2 x_{1}+3 x_{2} \leq 90 ; x_{1}, x_{2} \geq 0 \)
3) \( \operatorname{Max} Z=4 x_{1}+x_{2}+3 x_{3}+5 x_{4} \) s.t. \( 4 x_{1}-6 x_{2}-5 x_{3}+4 x_{4} \geq-20 \);
\( 3 x_{1}-2 x_{2}+4 x_{3}+x_{4} \leq 10 ; 8 x_{1}-3 x_{2}+3 x_{3}+2 x_{4} \leq 20 ; x_{1}, x_{2}, x_{3}, x_{4} \geq 0 \)
4) \( \operatorname{Max} Z=30 x_{1}+25 x_{2} \), st. \( 25 x_{1}+20 x_{2} \leq 80 ; 20 x_{1}+25 x_{2} \leq 90 ; x_{1}, x_{2} \geq 0 \)
5) \( \operatorname{Max} Z=10 x_{1}+5 x_{2} \), st. \( 5 x+2 x_{2} \leq 34 ; 4 x_{1}+4 x_{2} \leq 40 ; x_{1}, x_{2} \geq 0 \)
6) \( \operatorname{Max} Z=30 x_{1}+25 x_{2}+20 x_{3} \), st. \( 25 x_{1}+10 x_{2}+15 x_{3} \leq 80 ; 20 x_{1}+25 x_{2}+10 x_{3} \leq 90 ; x_{1}, x_{2}, x_{3} \geq \) 0
7) Max \( Z=3 x_{1}+2 x_{2}+x_{3} \), st. \( 2 x_{1}+x_{2} \leq 60 ; 2 x_{2}+x_{3} \leq 80 ; 10 x_{1}+15 x_{2}+20 x_{3} \leq 100 ; x_{1}+x_{2}+ \) \( 2 x_{3} \leq 90 ; x_{1}, x_{2}, x_{3} \geq 0 \).
